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Broderick Crawford - One of the best experts on this subject based on the ideXlab platform.
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A binary monkey search algorithm variation for solving the Set Covering Problem
Natural Computing, 2019Co-Authors: Broderick Crawford, Ricardo Soto, Fernando Paredes, Carlos Castro, Rodrigo Olivares, Wenceslao Palma, Gabriel Embry, Diego Flores, José-miguel RubioAbstract:In complexity theory, there is a widely studied grouping of optimization Problems that belongs to the non-deterministic polynomial-time hard Set. One of them is the Set Covering Problem, known as one of Karp’s 21 $${\mathscr {NP}}$$ NP -complete Problems, and it consists of finding a subSet of decision variables for satisfying a Set of constraints at the minimum feasible cost. However, due to the nature of the Problem, this cannot be solved using traditional complete algorithms for hard instances. In this work, we present an improved binary version of the monkey search algorithm for solving the Set Covering Problem. Originally, this approximate method was naturally inspired by the cognitive behavior of monkeys for climbing mountains. We propose a new climbing process with a better exploratory capability and a new cooperation procedure to reduce the number of unfeasible solutions. For testing this approach, we present a detailed computational results section, where we illustrate how this variation of the monkey search algorithm is capable of reaching various global optimums for a well-known instance Set from the Beasley’s OR-Library and how it outperforms many other heuristics and meta-heuristics addressed in the literature. Moreover, we add a complete statistical analysis to show the effectiveness of the proposed approach with respect to the original version.
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an adaptive intelligent water drops algorithm for Set Covering Problem
International Conference on Computational Science and Its Applications, 2019Co-Authors: Broderick Crawford, Ricardo Soto, Gino Astorga, Sanjay Misra, Jose Lemusromani, José-miguel RubioAbstract:Today, natural resources are more scarce than ever, so we must make good use of them. To achieve this goal, we can use metaheuristic optimization tools as an alternative to achieve good results in a reasonable amount of time. The present work focuses on the use of adaptive techniques to facilitate the use of this type of tool to obtain good functional parameters. We use a constructive metaheuristic algorithm called Intelligent Water Drops to solve the Set Covering Problem. To demonstrate the efficiency of the proposed method, the obtained results were compared with the standard version using the same initial configuration for both algorithms. Additionally, the Kolmogorov-Smirnov-Lilliefors, Wilcoxon signed-rank and Violin chart tests were applied to statistically validate the results, which showed that metaheuristics with autonomous search have a better behavior than do standard algorithms.
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a meta optimization approach to solve the Set Covering Problem
Ingeniería, 2018Co-Authors: Gino Astorga, Broderick Crawford, Ricardo Soto, Jose Garcia, Eric Monfroy, Enrique CortesAbstract:espanolContexto: En la industria los recursos son cada vez mas escasos. Por esta razon debemos hacer un buen uso de ellos.Siendo las herramientas de optimizacion una buena alternativa que se debe tener presente. Un Problema del mundo real lo contituye la ubicacion de instalaciones siendo el Problema de Cobertura de Conjuntos uno de los modelos mas utilizados. Nuestro interes, es encontrar alternativas de solucion a este Problema de la vida-real utilizando metaheuristicas.Metodo: Uno de los principales Problemas a que nos vemos enfrentados al utilizar metaheuristicas es la dificultad de realizar una correcta parametrizacion con el objetivo de encontrar buenas soluciones. Esta no es una tarea facil, para lo cual nuestra propuesta es utilizar una metaheuristica que permita proporcionar buenos parametros a otra metaheurstica que sera la encargada de resolver el Problema de Cobertura de Conjuntos.Resultados: Para probar nuestra propuesta, utilizamos el Set de 65 instancias de OR-Library el cual ademas fue comparado con otros recientes algoritmos utilizados para resolver el Problema de Cobertura de Conjuntos.Conclusiones: Nuestra propuesta a demostrado ser muy efectiva logrando producir soluciones de buena calidad evitando ademas que se tenga que invertir gran cantidad de tiempo en la parametrizacion de la metaheuristica encargada de resolver el Problema. EnglishContext: In the industry the resources are increasingly scarce. For this reason, we must make a gooduse of it. Being the optimization tools, a good alternative that it is necessary to bear in mind. A realworldProblem is the facilities location being the Set Covering Problem, one of the most used models.Our interest, it is to find solution alternatives to this Problem of the real-world using metaheuristics.Method: One of the main Problems which we turn out to be faced on having used metaheuristic is thedifficulty of realizing a correct parametrization with the purpose to find good solutions. This is not aneasy task, for which our proposal is to use a metaheuristic that allows to provide good parameters toanother metaheuristics that will be responsible for resolving the Set Covering Problem.Results: To prove our proposal, we use the Set of 65 instances of OR-Library which also was comparedwith other recent algorithms, used to solve the Set Covering Problem.Conclusions: Our proposal has proved to be very effective able to produce solutions of good qualityavoiding also have to invest large amounts of time in the parametrization of the metaheuristic responsiblefor resolving the Problem.
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adaptive black hole algorithm for solving the Set Covering Problem
Mathematical Problems in Engineering, 2018Co-Authors: Ricardo Soto, Broderick Crawford, Carlos Castro, Rodrigo Olivares, Ignacio Figueroa, Carla Taramasco, Alvaro Gomez, Fernando ParedesAbstract:Evolutionary algorithms have been used to solve several optimization Problems, showing an efficient performance. Nevertheless, when these algorithms are applied they present the difficulty to decide on the appropriate values of their parameters. Typically, parameters are specified before the algorithm is run and include population size, selection rate, and operator probabilities. This process is known as offline control and is even considered as an optimization Problem in itself. On the other hand, parameter Settings or control online is a variation of the algorithm original version. The main idea is to vary the parameters so that the algorithm of interest can provide the best convergence rate and thus may achieve the best performance. In this paper, we propose an adaptive black hole algorithm able to dynamically adapt its population according to solving performance. For that, we use autonomous search which appeared as a new technique that enables the Problem solver to control and adapt its own parameters and heuristics during solving in order to be more efficient without the knowledge of an expert user. In order to test this approach, we resolve the Set Covering Problem which is a classical optimization benchmark with many industrial applications such as line balancing production, crew scheduling, service installation, and databases, among several others. We illustrate encouraging experimental results, where the proposed approach is able to reach various global optimums for a well-known instance Set from Beasley’s OR-Library, while improving various modern metaheuristics.
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constructive metaheuristics for the Set Covering Problem
International Conference on Bioinspired Methods and Their Applications, 2018Co-Authors: Broderick Crawford, Ricardo Soto, Jose Garcia, Gino AstorgaAbstract:Different criteria exist for the classification of the metaheuristics. One important classification is: improvement metaheuristics and constructive. On the one hand improvement metaheuristics, begins with an initial solution and iteratively improves the quality of the solution using neighborhood search. On the other hand, constructive metaheuristics, are those in which a solution is built from the beginning, finding in each iteration a local optimum. In this article, we to compare two constructive metaheuristics, Ant Colony Optimization and Intelligent Water Drops, by solving a classical NP-hard Problem, such like the Set Covering Problem, which has many practical applications, including line balancing production, service installation and crew scheduling in railway, among others. The results reveal that Ant Colony Optimization has a better behavior than Intelligent Water Drops in relation to the Problem considered.
Fernando Paredes - One of the best experts on this subject based on the ideXlab platform.
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A binary monkey search algorithm variation for solving the Set Covering Problem
Natural Computing, 2019Co-Authors: Broderick Crawford, Ricardo Soto, Fernando Paredes, Carlos Castro, Rodrigo Olivares, Wenceslao Palma, Gabriel Embry, Diego Flores, José-miguel RubioAbstract:In complexity theory, there is a widely studied grouping of optimization Problems that belongs to the non-deterministic polynomial-time hard Set. One of them is the Set Covering Problem, known as one of Karp’s 21 $${\mathscr {NP}}$$ NP -complete Problems, and it consists of finding a subSet of decision variables for satisfying a Set of constraints at the minimum feasible cost. However, due to the nature of the Problem, this cannot be solved using traditional complete algorithms for hard instances. In this work, we present an improved binary version of the monkey search algorithm for solving the Set Covering Problem. Originally, this approximate method was naturally inspired by the cognitive behavior of monkeys for climbing mountains. We propose a new climbing process with a better exploratory capability and a new cooperation procedure to reduce the number of unfeasible solutions. For testing this approach, we present a detailed computational results section, where we illustrate how this variation of the monkey search algorithm is capable of reaching various global optimums for a well-known instance Set from the Beasley’s OR-Library and how it outperforms many other heuristics and meta-heuristics addressed in the literature. Moreover, we add a complete statistical analysis to show the effectiveness of the proposed approach with respect to the original version.
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adaptive black hole algorithm for solving the Set Covering Problem
Mathematical Problems in Engineering, 2018Co-Authors: Ricardo Soto, Broderick Crawford, Carlos Castro, Rodrigo Olivares, Ignacio Figueroa, Carla Taramasco, Alvaro Gomez, Fernando ParedesAbstract:Evolutionary algorithms have been used to solve several optimization Problems, showing an efficient performance. Nevertheless, when these algorithms are applied they present the difficulty to decide on the appropriate values of their parameters. Typically, parameters are specified before the algorithm is run and include population size, selection rate, and operator probabilities. This process is known as offline control and is even considered as an optimization Problem in itself. On the other hand, parameter Settings or control online is a variation of the algorithm original version. The main idea is to vary the parameters so that the algorithm of interest can provide the best convergence rate and thus may achieve the best performance. In this paper, we propose an adaptive black hole algorithm able to dynamically adapt its population according to solving performance. For that, we use autonomous search which appeared as a new technique that enables the Problem solver to control and adapt its own parameters and heuristics during solving in order to be more efficient without the knowledge of an expert user. In order to test this approach, we resolve the Set Covering Problem which is a classical optimization benchmark with many industrial applications such as line balancing production, crew scheduling, service installation, and databases, among several others. We illustrate encouraging experimental results, where the proposed approach is able to reach various global optimums for a well-known instance Set from Beasley’s OR-Library, while improving various modern metaheuristics.
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Solving the non-unicost Set Covering Problem by using cuckoo search and black hole optimization
Natural Computing, 2017Co-Authors: Ricardo Soto, Broderick Crawford, Fernando Paredes, Franklin Johnson, Rodrigo Olivares, Jorge Barraza, Ignacio Figueroa, Eduardo OlguínAbstract:The Set Covering Problem is a classical optimization benchmark that finds application in several real-world domains, particularly in line balancing production, crew scheduling, and service installation. The Problem consists in finding a subSet of columns in a zero-one matrix such that they cover all the rows of the matrix at a minimum cost. In this paper, we present two new approaches for efficiently solving this Problem, the first one based on cuckoo search and the second one on black hole optimization. Both are relatively modern bio-inspired metaheuristics that have attracted much attention due to their rapid convergence, easy implementation, and encouraging obtained results. We integrate to the core of both metaheuristics an effective pre-processing phase as well as multiple transfer functions and discretization methods. Pre-processing is employed for filtering the values from domains leading to infeasible solutions, while transfers function and discretization methods are used for efficiently handling the binary nature of the Problem. We illustrate interesting experimental results where the two proposed approaches are able to obtain various global optimums for a Set of well-known Set Covering Problem instances, outperforming also several recently reported techniques.
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analyzing the effects of binarization techniques when solving the Set Covering Problem through swarm optimization
Expert Systems With Applications, 2017Co-Authors: Jose M Lanzagutierrez, Broderick Crawford, Ricardo Soto, Natalia Berrios, Juan A Gomezpulido, Fernando ParedesAbstract:Abstract The Set Covering Problem (SCP) is one of the classical Karp’s 21 NP-complete Problems. Although this is a traditional optimization Problem, we find many papers assuming metaheuristics for solving the SCP in the current literature. However, while the SCP is a discrete Problem, most metaheuristics are defined for solving continuous optimization Problems, specially Swarm Intelligence Algorithms (SIAs). Hence, such algorithms should be adapted for working on the discrete scope, but most authors did not perform any study to select a concrete binarization approach. This situation might lead to the conclusion that selecting a concrete binarization technique does not influence the behavior of the algorithm, but rather the general approach of the metaheuristic. This circumstance led us to write this paper focusing on the inherent difficulty in binarization of metaheuristics designed for continuous optimization, when solving a discrete optimization Problem, concretely the SCP. To this end, we consider a recent SIA inspired by the behavior of cats and adapted to the discrete scope, which is called Binary Cat Swarm Optimization (BCSO). We replace the binarization technique assumed in the original BCSO by forty different approaches from the current literature. The results obtained while solving a standard SCP benchmark are analyzed through a widely accepted statistical method, concluding that it is crucial to select an adequate binarization approach to ensure that the solving algorithm reaches its full potential. Thus, the task of adapting a metaheuristic to the discrete scope is not a simple matter and should be carefully studied. To this end and as a result of this study, we give some recommendations to perform this task.
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solving the Set Covering Problem with binary cat swarm optimization
International Conference on Swarm Intelligence, 2016Co-Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Franklin Johnson, Fernando ParedesAbstract:The Set Covering Problem is a formal model for many practical optimization Problems. It consists in finding a subSet of columns in a zero---one matrix such that they cover all the rows of the matrix at a minimum cost. To solve the Set Covering Problem we use a metaheuristic called Binary Cat Swarm Optimization. This metaheuristic is a binary version of Cat Swarm Optimization generated by observing cat behavior. Cats have two modes of behavior: seeking mode and tracing mode. We are the first ones to use this metaheuristic to solve the Set Covering Problem, for this the proposed algorithm has been tested on 65 benchmarks instances.
Ricardo Soto - One of the best experts on this subject based on the ideXlab platform.
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A binary monkey search algorithm variation for solving the Set Covering Problem
Natural Computing, 2019Co-Authors: Broderick Crawford, Ricardo Soto, Fernando Paredes, Carlos Castro, Rodrigo Olivares, Wenceslao Palma, Gabriel Embry, Diego Flores, José-miguel RubioAbstract:In complexity theory, there is a widely studied grouping of optimization Problems that belongs to the non-deterministic polynomial-time hard Set. One of them is the Set Covering Problem, known as one of Karp’s 21 $${\mathscr {NP}}$$ NP -complete Problems, and it consists of finding a subSet of decision variables for satisfying a Set of constraints at the minimum feasible cost. However, due to the nature of the Problem, this cannot be solved using traditional complete algorithms for hard instances. In this work, we present an improved binary version of the monkey search algorithm for solving the Set Covering Problem. Originally, this approximate method was naturally inspired by the cognitive behavior of monkeys for climbing mountains. We propose a new climbing process with a better exploratory capability and a new cooperation procedure to reduce the number of unfeasible solutions. For testing this approach, we present a detailed computational results section, where we illustrate how this variation of the monkey search algorithm is capable of reaching various global optimums for a well-known instance Set from the Beasley’s OR-Library and how it outperforms many other heuristics and meta-heuristics addressed in the literature. Moreover, we add a complete statistical analysis to show the effectiveness of the proposed approach with respect to the original version.
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an adaptive intelligent water drops algorithm for Set Covering Problem
International Conference on Computational Science and Its Applications, 2019Co-Authors: Broderick Crawford, Ricardo Soto, Gino Astorga, Sanjay Misra, Jose Lemusromani, José-miguel RubioAbstract:Today, natural resources are more scarce than ever, so we must make good use of them. To achieve this goal, we can use metaheuristic optimization tools as an alternative to achieve good results in a reasonable amount of time. The present work focuses on the use of adaptive techniques to facilitate the use of this type of tool to obtain good functional parameters. We use a constructive metaheuristic algorithm called Intelligent Water Drops to solve the Set Covering Problem. To demonstrate the efficiency of the proposed method, the obtained results were compared with the standard version using the same initial configuration for both algorithms. Additionally, the Kolmogorov-Smirnov-Lilliefors, Wilcoxon signed-rank and Violin chart tests were applied to statistically validate the results, which showed that metaheuristics with autonomous search have a better behavior than do standard algorithms.
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a meta optimization approach to solve the Set Covering Problem
Ingeniería, 2018Co-Authors: Gino Astorga, Broderick Crawford, Ricardo Soto, Jose Garcia, Eric Monfroy, Enrique CortesAbstract:espanolContexto: En la industria los recursos son cada vez mas escasos. Por esta razon debemos hacer un buen uso de ellos.Siendo las herramientas de optimizacion una buena alternativa que se debe tener presente. Un Problema del mundo real lo contituye la ubicacion de instalaciones siendo el Problema de Cobertura de Conjuntos uno de los modelos mas utilizados. Nuestro interes, es encontrar alternativas de solucion a este Problema de la vida-real utilizando metaheuristicas.Metodo: Uno de los principales Problemas a que nos vemos enfrentados al utilizar metaheuristicas es la dificultad de realizar una correcta parametrizacion con el objetivo de encontrar buenas soluciones. Esta no es una tarea facil, para lo cual nuestra propuesta es utilizar una metaheuristica que permita proporcionar buenos parametros a otra metaheurstica que sera la encargada de resolver el Problema de Cobertura de Conjuntos.Resultados: Para probar nuestra propuesta, utilizamos el Set de 65 instancias de OR-Library el cual ademas fue comparado con otros recientes algoritmos utilizados para resolver el Problema de Cobertura de Conjuntos.Conclusiones: Nuestra propuesta a demostrado ser muy efectiva logrando producir soluciones de buena calidad evitando ademas que se tenga que invertir gran cantidad de tiempo en la parametrizacion de la metaheuristica encargada de resolver el Problema. EnglishContext: In the industry the resources are increasingly scarce. For this reason, we must make a gooduse of it. Being the optimization tools, a good alternative that it is necessary to bear in mind. A realworldProblem is the facilities location being the Set Covering Problem, one of the most used models.Our interest, it is to find solution alternatives to this Problem of the real-world using metaheuristics.Method: One of the main Problems which we turn out to be faced on having used metaheuristic is thedifficulty of realizing a correct parametrization with the purpose to find good solutions. This is not aneasy task, for which our proposal is to use a metaheuristic that allows to provide good parameters toanother metaheuristics that will be responsible for resolving the Set Covering Problem.Results: To prove our proposal, we use the Set of 65 instances of OR-Library which also was comparedwith other recent algorithms, used to solve the Set Covering Problem.Conclusions: Our proposal has proved to be very effective able to produce solutions of good qualityavoiding also have to invest large amounts of time in the parametrization of the metaheuristic responsiblefor resolving the Problem.
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adaptive black hole algorithm for solving the Set Covering Problem
Mathematical Problems in Engineering, 2018Co-Authors: Ricardo Soto, Broderick Crawford, Carlos Castro, Rodrigo Olivares, Ignacio Figueroa, Carla Taramasco, Alvaro Gomez, Fernando ParedesAbstract:Evolutionary algorithms have been used to solve several optimization Problems, showing an efficient performance. Nevertheless, when these algorithms are applied they present the difficulty to decide on the appropriate values of their parameters. Typically, parameters are specified before the algorithm is run and include population size, selection rate, and operator probabilities. This process is known as offline control and is even considered as an optimization Problem in itself. On the other hand, parameter Settings or control online is a variation of the algorithm original version. The main idea is to vary the parameters so that the algorithm of interest can provide the best convergence rate and thus may achieve the best performance. In this paper, we propose an adaptive black hole algorithm able to dynamically adapt its population according to solving performance. For that, we use autonomous search which appeared as a new technique that enables the Problem solver to control and adapt its own parameters and heuristics during solving in order to be more efficient without the knowledge of an expert user. In order to test this approach, we resolve the Set Covering Problem which is a classical optimization benchmark with many industrial applications such as line balancing production, crew scheduling, service installation, and databases, among several others. We illustrate encouraging experimental results, where the proposed approach is able to reach various global optimums for a well-known instance Set from Beasley’s OR-Library, while improving various modern metaheuristics.
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constructive metaheuristics for the Set Covering Problem
International Conference on Bioinspired Methods and Their Applications, 2018Co-Authors: Broderick Crawford, Ricardo Soto, Jose Garcia, Gino AstorgaAbstract:Different criteria exist for the classification of the metaheuristics. One important classification is: improvement metaheuristics and constructive. On the one hand improvement metaheuristics, begins with an initial solution and iteratively improves the quality of the solution using neighborhood search. On the other hand, constructive metaheuristics, are those in which a solution is built from the beginning, finding in each iteration a local optimum. In this article, we to compare two constructive metaheuristics, Ant Colony Optimization and Intelligent Water Drops, by solving a classical NP-hard Problem, such like the Set Covering Problem, which has many practical applications, including line balancing production, service installation and crew scheduling in railway, among others. The results reveal that Ant Colony Optimization has a better behavior than Intelligent Water Drops in relation to the Problem considered.
Paolo Toth - One of the best experts on this subject based on the ideXlab platform.
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an electromagnetism metaheuristic for the unicost Set Covering Problem
European Journal of Operational Research, 2010Co-Authors: Zahra Najiazimi, Paolo Toth, Laura GalliAbstract:In this paper we propose a new heuristic algorithm to solve the unicost version of the well-known Set Covering Problem. The method is based on the electromagnetism metaheuristic approach which, after generating a pool of solutions to create the initial population, applies a fixed number of local search and movement iterations based on the "electromagnetism" theory. In addition to some random aspects, used in the construction and local search phases, we also apply mutation in order to further escape from local optima. The proposed algorithm has been tested over 80 instances of the literature. On the classical benchmark instances, where the number of columns is larger than the number of rows, the algorithm, by using a fixed Set of parameters, always found the best known solution, and for 12 instances it was able to improve the current best solution. By using different parameter Settings the algorithm improved 4 additional best known solutions. Moreover, we proved the effectiveness of the electromagnetism metaheuristic approach for the unicost Set Covering Problem by embedding the procedures of the proposed algorithm in a genetic algorithm scheme. The worse results obtained by the genetic algorithm show the impact of the electromagnetism metaheuristic approach in conducting the search of the solution space by applying the movements based on the electromagnetism theory. Finally, we report the results obtained by modifying the proposed electromagnetism metaheuristic algorithm for solving the non-unicost Set Covering Problem.
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algorithms for the Set Covering Problem
Annals of Operations Research, 2000Co-Authors: Alberto Caprara, Paolo Toth, Matteo FischettiAbstract:The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and mass-transit companies. In this survey, we focus our attention on the most recent and effective algorithms for SCP, considering both heuristic and exact approaches, outlining their main characteristics and presenting an experimental comparison on the test-bed instances of Beasley's OR Library.
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a heuristic method for the Set Covering Problem
Operations Research, 1999Co-Authors: Alberto Caprara, Matteo Fischetti, Paolo TothAbstract:We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows an...
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a heuristic algorithm for the Set Covering Problem
Integer Programming and Combinatorial Optimization, 1996Co-Authors: Alberto Caprara, Matteo Fischetti, Paolo TothAbstract:We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The main characteristics of the algorithm we propose are (1) a dynamic pricing scheme for the variables, akin to that used for solving large-scale LP's, to be coupled with subgradient optimization and greedy algorithms, and (2) the systematic use of column fixing to obtain improved solutions. Moreover, we propose a number of improvements on the standard way of defining the step-size and the ascent direction within the subgradient optimization procedure, and the scores within the greedy algorithms. Finally, an effective refining procedure is proposed. Extensive computational results show the effectiveness of the approach.
Markus Sinnl - One of the best experts on this subject based on the ideXlab platform.
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the generalized reserve Set Covering Problem with connectivity and buffer requirements
European Journal of Operational Research, 2021Co-Authors: Eduardo Alvarezmiranda, Marcos Goycoolea, Ivana Ljubic, Markus SinnlAbstract:Abstract The design of nature reserves is becoming, more and more, a crucial task for ensuring the conservation of endangered wildlife. In order to guarantee the preservation of species and a general ecological functioning, the designed reserves must typically verify a series of spatial requirements. Among the required characteristics, practitioners and researchers have pointed out two crucial aspects: (i) connectivity, so as to avoid spatial fragmentation, and (ii) the design of buffer zones surrounding (or protecting) so-called core areas. In this paper, we introduce the Generalized Reserve Set Covering Problem with Connectivity and Buffer Requirements. This Problem extends the classical Reserve Set Covering Problem and allows to address these two requirements simultaneously. A solution framework based on Integer Linear Programming and branch-and-cut is developed. The framework is enhanced by valid inequalities, a construction and a primal heuristic and local branching. The Problem and the framework are presented in a modular way to allow practitioners to select the constraints fitting to their needs and to analyze the effect of e.g., only enforcing connectivity or buffer zones. An extensive computational study on grid-graph instances and real-life instances based on data from three states of the U.S. and one region of Australia is carried out to assess the suitability of the proposed model to deal with the challenges faced by decision-makers in natural reserve design. In the study, we also analyze the effects on the structure of solutions when only enforcing connectivity or buffer zones or just solving a generalized version of the classical Reserve Set Covering Problem. The results show, on the one hand, the flexibility of the proposed models to provide solutions according to the decision-makers’ requirements, and on the other hand, the effectiveness of the devised algorithm for providing good solutions in reasonable computing times.
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the generalized reserve Set Covering Problem with connectivity and buffer requirements
arXiv: Optimization and Control, 2019Co-Authors: Eduardo Alvarezmiranda, Marcos Goycoolea, Ivana Ljubic, Markus SinnlAbstract:The design of nature reserves is becoming, more and more, a crucial task for ensuring the conservation of endangered wildlife. In order to guarantee the preservation of species and a general ecological functioning, the designed reserves must typically verify a series of spatial requirements. Among the required characteristics, practitioners and researchers have pointed out two crucial aspects: (i) connectivity, so as to avoid spatial fragmentation, and (ii) the design of buffer zones surrounding (or protecting) so-called core areas. In this paper, we introduce the Generalized Reserve Set Covering Problem with Connectivity and Buffer Requirements. This Problem extends the classical Reserve Set Covering Problem and allows to address these two requirements simultaneously. A solution framework based on Integer Linear Programming and branch-and-cut is developed. The framework is enhanced by valid inequalities, a construction and a primal heuristic and local branching. An extensive computational study on grid-graph instances and real-life instances based on data from three states of the U.S. and one region of Australia is carried out to assess the suitability of the proposed model to deal with the challenges faced by decision-makers in natural reserve design. The results show, on the one hand, the flexibility of the proposed models to provide solutions according to the decision-makers' requirements, and on the other hand, the effectiveness of the devised algorithm for providing' good solutions in reasonable computing times.
